The rate of melting depends on how alike the
particles (small components of the ingredients in
these desserts) are with respect to each other,
and how strongly these particles interact
with one another.

An example - ice made from pure water tends to
melt slowly at room temperature because water
molecules (particles of water) attract and
interact strongly with one another. Once the
molecules form connections with one another at low
temperatures and become ice crystals, it takes a
lot of energy to disrupt these connections (which
we can also call bonds) and therefore melt
the ice. By contrast, fats such as cooking oils
do not have particles that interact very strongly
with one another, and therefore require less
energy to go from a solid to a liquid. Complex
mixtures such as ice cream take a little more
thinking.

All three of the desserts you mentioned have
some dairy product, which is not a pure liquid at
room temperature. They are water mixtures, and
water mixtures, compared to pure water, tend to
freeze at lower temperatures because the bonds
between molecules in the mixture are not as strong
as the bonds between pure water molecules. If we
go a step further with this logic, these mixtures
should also melt faster than pure water ice
because of these weaker bonds. However, it
is not clear from the information above which of
the three melts the fastest because the rate of
melting would depend on the components in these
desserts.

Typically, ice cream contains more percentage
of dairy than ice milk, which typically contains a
lower percentage of dairy than sherbet. Therefore,
you may expect that ice cream melts the fastest
and sherbet melts the slowest. However, there
may be differences in the amount of dairy in, say,
ice cream from different companies/brands, which
would affect the melting rates.

I highly encourage you to test these principles
by buying all three types of desserts from the
same brand, measuring out the same amount for each
type, setting these at room temperature, and
recording the time it takes for the three
to melt.

Answer 2:

Is this going to be your science fair
project? Here are links by people who did
similar experiments:
link 1
link 2
link 3

Answer 3:

You should act like a scientist and do the
experiment yourself!

My prediction is that it will be ice cream,
because it has (I believe) a higher fat content
than the other two, and fat has a higher
melting point than water.